What is the difference between `lm(y ~ x*z)` and `(y ~ i(x*z))`, when x and z are both numeric variables?
1. the first one includes an interaction term between x and z, whereas the second uses the product of x and z as a predictor in the model.
2. the second one includes an interaction term between x and z, whereas the first uses the product of x and z as a predictor in the model.
3. the first includes only an interaction term for x and z, while the second includes both interaction effects and main effects.
4. the second includes only an interaction term for x and z, while the first includes both interaction effects and main effects.